Simply reducible groups have applications in physics and chemistry. Their structures depends on the irreducible representations. In this paper we consider a class of groups called Z -groups and 2-groups of maximal rank and also extra-special 2-groups and examine them for simple reducibility. In the end we examine some other classes of finite groups for being SR or ASR
{"title":"On simply reducible groups","authors":"Mohammad Reza Darafsheh, Manouchehr Misaghian","doi":"10.12988/ija.2023.91796","DOIUrl":"https://doi.org/10.12988/ija.2023.91796","url":null,"abstract":"Simply reducible groups have applications in physics and chemistry. Their structures depends on the irreducible representations. In this paper we consider a class of groups called Z -groups and 2-groups of maximal rank and also extra-special 2-groups and examine them for simple reducibility. In the end we examine some other classes of finite groups for being SR or ASR","PeriodicalId":13756,"journal":{"name":"International Journal of Algebra and Computation","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135601315","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Composition of primes in elliptic curves y2=x3-2px","authors":"Shin-wook Kim","doi":"10.12988/ija.2023.91743","DOIUrl":"https://doi.org/10.12988/ija.2023.91743","url":null,"abstract":"","PeriodicalId":13756,"journal":{"name":"International Journal of Algebra and Computation","volume":"109 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80878431","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We study the structure of certain von Neumann regular rings and π-regular rings with certain constraints such as having a prime and other constraints. For example, we prove that a π-regular ring with prime center is strongly π-regular, and other related results are also proved. An example is also given to illustrate our result
{"title":"On the structure of certain von Neumann regular and π-regular rings with prime center","authors":"H. Abu-Khuzam","doi":"10.12988/ija.2023.91738","DOIUrl":"https://doi.org/10.12988/ija.2023.91738","url":null,"abstract":"We study the structure of certain von Neumann regular rings and π-regular rings with certain constraints such as having a prime and other constraints. For example, we prove that a π-regular ring with prime center is strongly π-regular, and other related results are also proved. An example is also given to illustrate our result","PeriodicalId":13756,"journal":{"name":"International Journal of Algebra and Computation","volume":"86 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73384993","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Correlating results of ranks in elliptic curves to matrix ring","authors":"Shin-wook Kim","doi":"10.12988/ija.2023.91742","DOIUrl":"https://doi.org/10.12988/ija.2023.91742","url":null,"abstract":"Suppose that 𝐸 −2𝑝 and 𝐸 −𝑝 and 𝐸 −3𝑝 are elliptic curves 𝑦 2 = 𝑥 3 − 2𝑝𝑥 and 𝑦 2 = 𝑥 3 − 𝑝𝑥 and 𝑦 2 = 𝑥 3 − 3𝑝𝑥 with prime 𝑝 then","PeriodicalId":13756,"journal":{"name":"International Journal of Algebra and Computation","volume":"100 10","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72559914","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
E. Salinas-Hernández, Cesar R. Martinez-Garcia, M. A. Leon-Hernandez
In this work we develop the generalized cross product, in a different way from what has been reported in several research works
在这项工作中，我们发展了广义叉积，以不同于其他研究工作的方式
{"title":"New approach to the generalized cross product. Orthonormal sets and Cramer's rule","authors":"E. Salinas-Hernández, Cesar R. Martinez-Garcia, M. A. Leon-Hernandez","doi":"10.12988/ija.2023.91774","DOIUrl":"https://doi.org/10.12988/ija.2023.91774","url":null,"abstract":"In this work we develop the generalized cross product, in a different way from what has been reported in several research works","PeriodicalId":13756,"journal":{"name":"International Journal of Algebra and Computation","volume":"39 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78666162","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Ranks in curves y2=x3-2px with primes","authors":"Shin-wook Kim","doi":"10.12988/ija.2023.91744","DOIUrl":"https://doi.org/10.12988/ija.2023.91744","url":null,"abstract":"","PeriodicalId":13756,"journal":{"name":"International Journal of Algebra and Computation","volume":"336 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73142638","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Ranks in curves y2=x3-37px and y2=x3-61px and y2=x3-67px and y2=x3-83px and y2=x3-947px","authors":"Shin-wook Kim","doi":"10.12988/ija.2023.91745","DOIUrl":"https://doi.org/10.12988/ija.2023.91745","url":null,"abstract":"","PeriodicalId":13756,"journal":{"name":"International Journal of Algebra and Computation","volume":"38 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83002350","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-12-06DOI: 10.1142/s021819672350056x
Eonkyung Lee, Sangjin Lee
The action of a right-angled Artin group on its extension graph is known to be acylindrical because the cardinality of the so-called $r$-quasi-stabilizer of a pair of distant points is bounded above by a function of $r$. The known upper bound of the cardinality is an exponential function of $r$. In this paper we show that the $r$-quasi-stabilizer is a subset of a cyclic group and its cardinality is bounded above by a linear function of $r$. This is done by exploring lattice theoretic properties of group elements, studying prefixes of powers and extending the uniqueness of quasi-roots from word length to star length. We also improve the known lower bound for the minimal asymptotic translation length of a right angled Artin group on its extension graph.
{"title":"Acylindricity of the action of right-angled Artin groups on extension graphs","authors":"Eonkyung Lee, Sangjin Lee","doi":"10.1142/s021819672350056x","DOIUrl":"https://doi.org/10.1142/s021819672350056x","url":null,"abstract":"The action of a right-angled Artin group on its extension graph is known to be acylindrical because the cardinality of the so-called $r$-quasi-stabilizer of a pair of distant points is bounded above by a function of $r$. The known upper bound of the cardinality is an exponential function of $r$. In this paper we show that the $r$-quasi-stabilizer is a subset of a cyclic group and its cardinality is bounded above by a linear function of $r$. This is done by exploring lattice theoretic properties of group elements, studying prefixes of powers and extending the uniqueness of quasi-roots from word length to star length. We also improve the known lower bound for the minimal asymptotic translation length of a right angled Artin group on its extension graph.","PeriodicalId":13756,"journal":{"name":"International Journal of Algebra and Computation","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42009397","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-11-24DOI: 10.1142/s0218196723500534
M. Elder, Adam Piggott, K. Townsend
We call a graph $k$-geodetic, for some $kgeq 1$, if it is connected and between any two vertices there are at most $k$ geodesics. It is shown that any hyperbolic group with a $k$-geodetic Cayley graph is virtually-free. Furthermore, in such a group the centraliser of any infinite order element is an infinite cyclic group. These results were known previously only in the case that $k=1$. A key tool used to develop the theorem is a new graph theoretic result concerning ``ladder-like structures'' in a $k$-geodetic graph.
{"title":"On k-geodetic graphs and groups","authors":"M. Elder, Adam Piggott, K. Townsend","doi":"10.1142/s0218196723500534","DOIUrl":"https://doi.org/10.1142/s0218196723500534","url":null,"abstract":"We call a graph $k$-geodetic, for some $kgeq 1$, if it is connected and between any two vertices there are at most $k$ geodesics. It is shown that any hyperbolic group with a $k$-geodetic Cayley graph is virtually-free. Furthermore, in such a group the centraliser of any infinite order element is an infinite cyclic group. These results were known previously only in the case that $k=1$. A key tool used to develop the theorem is a new graph theoretic result concerning ``ladder-like structures'' in a $k$-geodetic graph.","PeriodicalId":13756,"journal":{"name":"International Journal of Algebra and Computation","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46304848","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-09-08DOI: 10.1142/S0218196723500583
D. Berlyne
We provide an explicit construction that allows one to easily decompose a graph braid group as a graph of groups. This allows us to compute the braid groups of a wide range of graphs, as well as providing two general criteria for a graph braid group to split as a non-trivial free product, answering two questions of Genevois. We also use this to distinguish certain right-angled Artin groups and graph braid groups. Additionally, we provide an explicit example of a graph braid group that is relatively hyperbolic, but is not hyperbolic relative to braid groups of proper subgraphs. This answers another question of Genevois in the negative.
{"title":"Graph of groups decompositions of graph braid groups","authors":"D. Berlyne","doi":"10.1142/S0218196723500583","DOIUrl":"https://doi.org/10.1142/S0218196723500583","url":null,"abstract":"We provide an explicit construction that allows one to easily decompose a graph braid group as a graph of groups. This allows us to compute the braid groups of a wide range of graphs, as well as providing two general criteria for a graph braid group to split as a non-trivial free product, answering two questions of Genevois. We also use this to distinguish certain right-angled Artin groups and graph braid groups. Additionally, we provide an explicit example of a graph braid group that is relatively hyperbolic, but is not hyperbolic relative to braid groups of proper subgraphs. This answers another question of Genevois in the negative.","PeriodicalId":13756,"journal":{"name":"International Journal of Algebra and Computation","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45168616","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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